A simple example for comparing GENERIC with rational non-equilibrium thermodynamics

During the last 15 years a bracket formalism of dissipative continuum physics has been developed which resulted in a formulation which is shortly denoted as GENERIC. GENERIC has been applied to different problems of continuum thermodynamics, often in this way, that a well-known problem was reformulated in GENERIC formalism. To learn some more about the GENERIC procedure we consider a gas which is contained in a cylinder closed by a piston moving with friction. We treat this simple discrete system with rational non-equilibrium thermodynamics by using Liu's procedure and, for comparison, also with the GENERIC formalism. Both different procedures yield in the same results, especially in the same entropy production. Differences, similarities and fundamental presuppositions of both formalisms are discussed and compared.

[1]  D. Jou,et al.  Nonlinear and Hamiltonian extended irreversible thermodynamics , 1998 .

[2]  Brian J. Edwards,et al.  Non-canonical Poisson bracket for nonlinear elasticity with extensions to viscoelasticity , 1991 .

[3]  W. Muschik,et al.  On extended thermodynamics of discrete systems , 1996 .

[4]  I-Shih Liu,et al.  Method of Lagrange multipliers for exploitation of the entropy principle , 1972 .

[5]  W. Muschik,et al.  An Amendment to the Second Law , 1996 .

[6]  W. Muschik.  Irreversibility and Second Law , 1998 .

[7]  W. Muschik.  Empirical foundation and axiomatic treatment of non-equilibrium temperature , 1977 .

[8]  W. Muschik,et al.  A concept of non-equilibrium temperature , 1977 .

[9]  Bernard D. Coleman,et al.  Existence of Caloric Equations of State in Thermodynamics , 1964 .

[10]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. I. Development of a general formalism , 1997 .

[11]  W. Muschik.  Fundamentals of Nonequilibrium Thermodynamics , 1993 .

[12]  Hans Christian Öttinger,et al.  General projection operator formalism for the dynamics and thermodynamics of complex fluids , 1998 .

[13]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism , 1997 .

[14]  H. C. Öttinger,et al.  Time-structure invariance criteria for closure approximations , 1997 .

[15]  Miroslav Grmela,et al.  Bracket formulation of dissipative fluid mechanics equations , 1984 .